Put the oil in a three-quart-deep saucepan. Add onions and garlic and cook for two minutes. Add the remaining vegetables, and toss to coat with oil. Pour spaghetti sauce. Boil and simmer over a low fire, covered, for 10 minutes. Season with salt, sugar, and pepper.

Spoon 1/3 of the vegetable mixture onto the prepared pan. Lay six sheets of lasagna on top of the vegetable mixture. Spoon another third of the vegetable mixture. Top with the remaining lasagna sheets and the remaining vegetable mixture. Arrange the Quickmelt or mozzarella cheese on top. Dot with ricotta or cottage cheese. Bake at 400°F or 200°C for 30 minutes.